Derivation of the simplest transport equations for dissipation and vorticity from a modified equation for small-scale velocity

Abstract

Transport equations for dissipation and vorticity are derived from a transport equation for small-scale velocity, using expression for turbulent viscosity through dissipation and gradients of large-scale velocity, assuming validity of local turbulent energy balance. These equations are of simple form. The equations can be used for parametrization in the various turbulence models. The approach can be generalized for magnetohydrodynamics, the flow with variable fluid density, the non-newton flow, etc.